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## Über dieses Buch

Computational fluid dynamics, commonly known under the acronym 'CFD', is undergoing significant expansion in terms of both the number of courses offered at universities and the number of researchers active in the field. There are a number of software packages available that solve fluid flow problems; the market is not quite as large as the one for structural mechanics codes, in which the use of finite element methods is well established. The lag can be explained by the fact that CFD problems are, in general, more difficult to solve. However, CFD codes are slowly being accepted as design tools by industrial users. At present, users of CFD need to be fairly knowledgeable and this requires education of both students and working engineers. The present book is an attempt to fill this need. It is our belief that, to work in CFD, one needs a solid background in fluid mechanics and numerical analysis; significant errors have been made by peo­ ple lacking knowledge in one or the other. We therefore encourage the reader to obtain a working knowledge of these subjects before entering into a study of the material in this book. Because different people view numerical meth­ ods differently, and to make this work more self-contained, we have included two chapters on basic numerical methods in this book. The book is based on material offered by the authors in courses at Stanford University, the Uni­ versity of Erlangen-Niirnberg and the University of Hamburg.

## Inhaltsverzeichnis

### 1. Basic Concepts of Fluid Flow

Abstract
Fluids are substances whose molecular structure offers no resistance to external shear forces: even the smallest force causes deformation of a fluid particle. Although a significant distinction exists between liquids and gases, both types of fluids obey the same laws of motion. In most cases of interest, a fluid can be regarded as continuum, i.e. a continuous substance.
Joel H. Ferziger, Milovan Perić

### 2. Introduction to Numerical Methods

Abstract
As the first chapter stated, the equations of fluid mechanics — which have been known for over a century — are solvable for only a limited number of flows. The known solutions are extremely useful in helping to understand fluid flow but rarely can they be used directly in engineering analysis or design. The engineer has traditionally been forced to use other approaches.
Joel H. Ferziger, Milovan Perić

### 3. Finite Difference Methods

Abstract
As was mentioned in Chap. 1, all conservation equations have similar structure and may be regarded as special cases of a generic transport equation, Eq. (1.26), (1.27) or (1.28). For this reason, we shall treat only a single, generic conservation equation in this and the following chapters. It will be used to demonstrate discretization methods for the terms which are common to all conservation equations (convection, diffusion, and sources). The special features of the Navier-Stokes equations, and techniques for solving coupled non-linear problems will be introduced later. Also, for the time being, the unsteady term will be dropped so we shall consider only time-independent problems.
Joel H. Ferziger, Milovan Perić

### 4. Finite Volume Methods

Abstract
As in the previous chapter, we shall consider only the generic conservation equation for a quantity φ and assume that the velocity field and all fluid properties are known. The finite volume method uses the integral form of the conservation equation as the starting point:
$$\int_S \rho\phi\upsilon\,\cdot n\,{\text{d}}S = \int_S \Gamma\,{\text{grad}}\phi \cdot\,n\,{\text{d}}S + \int_{\Omega}\,q_{\phi}\,{\text{d}}\Omega.$$
(4.1)
Joel H. Ferziger, Milovan Perić

### 5. Solution of Linear Equation Systems

Abstract
In the previous two chapters we showed how the convection-diffusion equation may be discretized using FD and FV methods. In either case, the result of the discretization process is a system of algebraic equations, which are linear or non-linear according to the nature of the partial differential equation(s) from which they are derived. In the non-linear case, the discretized equations must be solved by an iterative technique that involves guessing a solution, linearizing the equations about that solution, and improving the solution; the process is repeated until a converged result is obtained. So, whether the equations are linear or not, efficient methods for solving linear systems of algebraic equations are needed.
Joel H. Ferziger, Milovan Perić

### 6. Methods for Unsteady Problems

Abstract
In computing unsteady flows, we have a fourth coordinate direction to consider: time. Just as with the space coordinates, time must be discretized. We can consider the time “grid” in either the finite difference spirit, as discrete points in time, or in a finite volume view as “time volumes”. The major difference between the space and time coordinates lies in the direction of influence: whereas a force at any space location may (in elliptic problems) influence the flow anywhere else, forcing at a given instant will affect the flow only in the future — there is no backward influence. Unsteady flows are, therefore, parabolic-like in time. This means that no conditions can be imposed on the solution (except at the boundaries) at any time after the initiation of the calculation, which has a strong influence on the choice of solution strategy. To be faithful to the nature of time, essentially all solution methods advance in time in a step-by-step or “marching” manner. These methods are very similar to ones applied to initial value problems for ordinary differential equations (ODEs) so we shall give a brief review of such methods in the next section.
Joel H. Ferziger, Milovan Perić

### 7. Solution of the Navier-Stokes Equations

Abstract
In Chaps. 3, 4 and 6 we dealt with the discretization of a generic conservation equation. The discretization principles described there apply to the momentum and continuity equations (which we shall collectively call the Navier-Stokes equations). In this chapter, we shall describe how the terms in the momentum equations which differ from those in the generic conservation equation are treated.
Joel H. Ferziger, Milovan Perić

### 8. Complex Geometries

Abstract
Most flows in engineering practice involve complex geometries which are not readily fit with Cartesian grids. Although the principles of discretization and solution methods for algebraic systems described earlier may be used, many modifications are required. The properties of the solution algorithm depend on the choices of the grid and of the vector and tensor components, and the arrangement of variables on the grid. These issues are discussed in this chapter.
Joel H. Ferziger, Milovan Perić

### 9. Turbulent Flows

Abstract
Most flows encountered in engineering practice are turbulent; they are characterized by the following properties:
• Turbulent flows are highly unsteady. A plot of the velocity as a function of time would appear random to an observer unfamiliar with these flows. The word ‘chaotic’ could be used but it has been given another definition in recent years.
• They are three-dimensional. The time-averaged velocity may be a function of only two coordinates, but the instantaneous field appears essentially random.
• They contain a great deal of vorticity. Stretching of vortices is one of the principal mechanisms by which the intensity of the turbulence is increased.
• Turbulence increases the rate at which conserved quantities are stirred. That is, parcels of fluid with differing concentrations of the conserved properties are brought into contact. The actual mixing is accomplished by diffusion. Nonetheless, this behavior is often called diffusive.
• By increasing the mixing of momentum, turbulence brings fluids of differing momentum content into contact. The reduction of the velocity gradients produced by the action of viscosity reduces the kinetic energy of the flow; in other words, it is dissipative. The lost energy is irreversibly converted into internal energy of the fluid.
• It has been shown in recent years that turbulent flows contain coherent structures — repeatable and essentially deterministic events that are responsible for a large part of the mixing. However, the random part of turbulent flows causes these events to differ from each other in size, strength, and time interval between occurrences, making study of them very difficult.
Joel H. Ferziger, Milovan Perić

### 10. Compressible Flow

Abstract
Compressible flows are important in aerodynamics and turbomachinery among other applications. In high speed flows around aircraft, the Reynolds numbers are extremely high and turbulence effects are confined to thin boundary layers. The drag consists of two components, frictional drag due to the boundary layer and pressure or form drag which is essentially inviscid in nature; there may also be wave drag due to shocks which may be computed from the inviscid equations provided that care is taken to assure that the second law of thermodynamics is obeyed. If frictional drag is ignored, these flows may be computed using the inviscid momentum Euler equations.
Joel H. Ferziger, Milovan Perić

### 11. Efficiency and Accuracy Improvement

Abstract
The best measure of the efficiency of a solution method is the computational effort required to achieve the desired accuracy. There are several methods for improving the efficiency and accuracy of CFD methods; we shall present three that are general enough to be applied to any of the solution schemes described in previous chapters.
Joel H. Ferziger, Milovan Perić

### 12. Special Topics

Abstract
In this chapter we briefly discuss some topics related to application of CFD in engineering practice. Many application areas require that some special phenomena or boundary conditions be taken into account; we shall address only few of them.
Joel H. Ferziger, Milovan Perić

### Backmatter

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